Update the app badge and clear read notifications on room list updates

The sync update action is sent from the room list service state listener,
which fires before the SDK has applied the new unread counts, leaving the
app badge one sync behind. Drive both the badge and the clearing of
delivered notifications for fully read rooms from the room list publisher
instead, moving the observer from the ChatsTabFlowCoordinator into the
UserSessionFlowCoordinator.

The NotificationManager now receives the badge count from the caller so the
same value can be reused elsewhere.

UnitTests/Sources/NotificationManager/NotificationManagerTests.swift

@@ -262,10 +262,8 @@ final class NotificationManagerTests {
     }
     
     @Test
-    func updatingAppBadgeCountUsesTheClientSideCount() async {
-        clientProxy.totalUnreadNotifications = 7
-        
-        await notificationManager.updateAppBadgeCount()
+    func updatingAppBadgeCount() async {
+        await notificationManager.updateAppBadgeCount(7)
         
         #expect(notificationCenter.setBadgeCountReceivedNewBadgeCount == 7)
         #expect(appSettings.lastKnownBadgeCount == 7)
@@ -275,7 +273,7 @@ final class NotificationManagerTests {
     func updatingAppBadgeCountWithoutASessionDoesNothing() async {
         notificationManager.setUserSession(nil)
         
-        await notificationManager.updateAppBadgeCount()
+        await notificationManager.updateAppBadgeCount(7)
         
         #expect(!notificationCenter.setBadgeCountCalled)
     }